PESHAWAR (Reuters) -- Two bombs have exploded in the northwestern Pakistani city of Peshawar, killing at least five people, a rescue official said, hours after the Taliban claimed an atack in Lahore the previous day and warned of more violence.

"We have shifted five dead bodies to the hospital trauma center and about 30 wounded are now in the emergency room," Zulfiqar Ahmed, an official with the Ehdi Rescue Center, told Reuters.

The blasts came a day after the suicide gun and bomb attack in Lahore killed 24 people and wounded nearly 300. The Pakistani Taliban claimed responsibility for that incident, saying it was a revenge for an army offensive in the Swat region.

"They were two bomb blasts. There are casualties, but I don't know the numbers. A building has caught fire," senior police officer Mohammad Anis told Reuters soon after the Peshawar bombings.

The bombs went off in a crowded market area of Peshawar's old city.

"I can see about 15 wounded people lying on the ground. People are running out of their shops," city resident Tahir Ali Shah told Reuters by telephone.

Militant violence in nuclear-armed Pakistan has surged since mid-2007, with numerous attacks on the security forces, as well as on government and Western targets.

The violence and a perception the government was being distracted by political squabbling and failing to act to stop the Taliban had alarmed the United States and other Western allies.

But the army moved against the Taliban in their Swat valley stronghold late last month after the militants had seized a district only 100 kilometers from the capital and a peace pact collapsed.

A militant commander loyal to Pakistani Taliban leader Baitullah Mehsud said earlier on May 28 the Lahore attack was to avenge the offensive in Swat.

"We have achieved our target. We were looking for this target for a long time. It was a reaction to the Swat operation," the commander, Hakimullah Mehsud, told Reuters by telephone from an undisclosed location.

The government also said the attack in a high-security area in Lahore where a police headquarters, emergency services building and a military intelligence office are located, was revenge for the Swat offensive.

Pakistan is vital for U.S. plans to defeat Al-Qaeda and cut support for the Afghan Taliban and the United States has been heartened by the Swat offensive and by public support for it.

"The response by the military so far has the support of the Pakistani people," White House national security adviser General James Jones said in Washington on May 27.

"The government's popularity has shot up a little bit in the polls and that is going to have an effect in the border region between Afghanistan and Pakistan," he said.

'Major Attacks'

But militant attacks in cities could undermine support for the offensive and Hakimullah Mehsud warned of more violence.

"We want the people of Lahore, Rawalpindi, Islamabad, and Multan to leave those cities as we plan major attacks against government facilities in coming days and weeks," he said.

The military released late on May 27 what it said was a tape of an intercepted telephone call between the Taliban spokesman in Swat, Muslim Khan, and an unidentified militant in which Khan urges revenge attacks.

"There's a need for them to strike soldiers in Punjab so that they can understand and feel pain," Khan says on the tape, broadcast on Pakistani television. "Strikes should be carried out on their homes so their kids get killed and then they'll realize."

The unidentified man said militants had been ordered to strike wherever they could.

The government has vowed to defeat the Taliban and on May 28 it published an offer of a reward of 5 million rupees ($60,000) for the capture, dead or alive, of the Taliban leader in Swat, Fazlullah, and smaller bounties for 20 of his comrades.

The military says about 1,100 militants and about 60 soldiers have been killed in the fighting in the Swat region. There has been no independent confirmation of those estimates.